Question

Which reason justifies Statement 5?

Answer 1

Here, from the diagram it is clear that a triangle XYZ is formed as the lines b,c and D intersect.

Also, wkt,

Sum of three angles of a triangle is always 180°

The above is the justification for statement 5

Answer 2

Reason given in explanation

Explanation:

1. Given : Lines A and B are parallel, C and D are transversals .

2. We know that if two lines are parallel then alternate interior angles are equal.

As lines A and B are parallel,
`\angle Y=\angle 4` (
`\angle Y , \angle 4` are alternate interior angles )

3. We know that if two lines are parallel then alternate interior angles are equal.

As lines A and B are parallel,
`\angle Z=\angle 6` (
`\angle Z , \angle 6` are alternate interior angles )

4. As
`\angle X\,,\,\angle 4\,,\,\angle 6` lie on a straight line,
`\angle X+\angle 4+\angle 6=180^(\circ)`

5. From point 2, 3, 4, we get

`\angle X+\angle 4+\angle 6=180^(\circ)\\\angle X+\angle Y+\angle Z=180^(\circ)`